20.500.12556/RUL-143949 Predstavitev polinomskih krivulj in ploskev s principom razcveta magistrsko delo Representation of polynomial curves and surfaces with the blossoming principle V delu predstavimo princip razcveta: za vsako polinomsko preslikavo F stopnje n med afinimi prostori obstaja simetrična, multiafina preslikava f v n spremenljivkah, ki se na diagonali ujema s prvotno preslikavo. Preslikavi f rečemo (multiafin) razcvet preslikave F. Z njo lahko vsako polinomsko krivuljo oz. ploskev predstavimo kot Bezierjevo krivuljo oz. trikotno Bezierjevo krpo. Pri tem so kontrolne točke krivulje oz. krpe določene z vrednostmi razcveta na izbranem afinem ogrodju prostora. S pomočjo razcveta obravnavamo tudi zlepke Bezierjevih krivulj oz. krp in njihovo gladkost. Pokažemo, da se pogoji za posamezen red gladkosti lahko izrazijo kot enakosti med razcveti obeh krivulj oz. krp pri ustreznih argumentih. In this work we present the blossoming principle: for every polynomial map F of degree n between affine spaces there exists a symmetric, multiaffine map f in n variables, which agrees with F on the diagonal. We call f the (multiaffine) blossom of F. With it we can represent each polynomial curve or surface as a Bezier curve or triangular Bezier patch. The control points of said curve or patch are determined by the values of the blossom f on a chosen affine frame. Utilising the blossoming principle, we also describe splines of Bezier curves and splines of triangular Bezier patches and their smoothness. We show that the conditions for a spline to satisfy a particular order of continuity can be expressed as equalities between the blossoms of both curves or surfaces on a specific collection of arguments. afin prostor polinom razcvet Bernsteinovi bazni polinomi Bezierjeve krivulje trikotne Bezierjeve krpe ploskev de Casteljaujev algoritem zlepki affine space polynomial blossom Bernstein basis polynomials Bezier curve triangular Bezier patch surface de Casteljau algorithm spline true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2023-01-22 08:15:02 2023-01-22 08:15:07 2024-05-29 10:50:46 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.6 130112 138055171 7665.pdf 7665.pdf 1 FBA86245B372D4422A0E2C5F5DDB0B5F b514a61442cd94d467c4b6fe3fe2731332b3fa26fb96155055095a4b738c08db 3f5742af-9a24-11ed-9c94-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=166010 Fakulteta za matematiko in fiziko 0 0 0